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THILLY 
The  Process  of  Inductive  Inference 

i^^H 

M 

Volume  II  JNumbee  3 


THE 


UNIVERSITY  OF  MISSOURI 

STUDIES 


EDITED    BY 

FRANK  THILLY 
Professor  of  Philosophy 


THE  PROCESS  OF  INDUCTIVE 
INFERENCE 


BY 


THE  EDITOR 


PUBLISHED    BY   THE 

UNIVERSITY  OF  MISSOURI 
April,   1904 

PRICE,  :i5  CENTS 


3 

THE  PROCESS  OF  INDUCTIVE 

INFERENCE 


J 


Volume  II  Kumbek  3 


THE 


UNIVERSITY  OF  MISSOURI 

STUDIES 


EDITED     BY 

FRANK  THILLY 

;/ 

Professor   of  Philosophy 


THE  PROCESS  OF  INDUCTIVE 
INFERENCE 


BY 


THE  EDITOR 


PUBLISHED    BY    THE 

UNIVERSITY  OF  MISSOURI 
April,    1904 

PRICE,  35  CENTS 


U^ 


V 


Copyright,  1904,  by 
THE   UNIVERSITY  OF  MISSOURI 


PRESS  OF  E.    W.   STEPHENS 
COLUMBIA,  MO. 


TABLE  OF  CONTENTS 


Part  I.     Historical  Survey 

Page 

§1.     Aristotle i 

§2.     Francis  Bacon        3 

§3.     John  Stuart  Mill 6 

§4.     W.  Stanley  Jevons 13 

§5.     Christoph  Sigwart 16 

§6.     Hermann  Lotze 21 

Part  II.     The  Theory  of  Induction 

§1.     Introduction 27 

§2.     The  Nature  of  Induction 29 

§3.     The  Validity  of  the  Process 36 


THE   PROCESS   OF  INDUCTIVE 
INFERENCE 


PART  I 
Historical  Survey 


§  I.  Aristotle  distinguishes  between  reasonings  which 
proceed  from  first  principles  and  reasonings  which  lead  up 
to  first  principles.!  The  first  kind  of  reasoning  is  the  syllogism, 
the  second  induction  (^iTzayajy-q') ,  Induction  is  a  passage 
from  particulars  to  universals,  "as  if  the  pilot  skilled  in  his  art 
is  the  best,  so  also  is  the  charioteer,  generally  the  skillful  is  the 
most  excellent  about  each  thing."  - 

^Nicomachean  Ethics,  Bk.  I,  chap  ii.  hXi.o,  Posterior  Analytics,  Bk. 
I,  chap,  xviii,  English  translation  in  Bohn's  library:  "It  is  clear  also 
that  if  any  sense  be  deficient,  a  certain  science  must  be  also  deficient, 
which  we  can  not  possess,  since  we  learn  either  by  induction  or  by  dem- 
onstration. Now  demonstration  is  from  universals,  but  induction  from 
particulars."     See  also,  Bk.  I,  chap,  i;  Bk.  II,  chap.  xix. 

^The  Topics,  Bk.  I,  chap,  xii,  English  translation  Bohn's  library: 
"These  things  then  being  determined,  we  must  distinguish  how  many 
species  of  dialectic  arguments  there  are.  Now  one  is  induction,  but  the 
other  syllogism,  and  what  indeed  syllogism  is,  has  been  declared  before, 
but  induction  is  a  progression  from  singulars  to  universals,  as  if  the  pilot 
skilled  in  his  art  is  the  best,  so  also  is  the  charioteer,  and  generally  the 
skillful  is  the  most  excellent  about  each  thing." 

149]  I 


2  UNIVERSITY  OF  MISSOURI  STUDIES  [^50 

But  what  right  have  we  to  pass  from  particulars  to  uni- 
versals?     Aristotle  seems  to  justify  the  procedure  in  two  ways. 
The  particular,  he  helieves,  arouses  in  the  mind  the  universal. 
We  perceive  the  particular,  c.  g.,  Callias,  but  perception  includes 
the  universal,  e.  g.,  man.^     That  is,  the  perception  of  the  particu- 
lar arouses  in  our  minds  the  idea  of  the  universal,  of  the  all. 
In  the  words  of  Thomas  Taylor,  a  translator  and  commentator 
of  Aristotle :     ''Induction  is  so  far  subservient  to  the  acquisi- 
tions of  science,  as  it  evocates  into  energy  in  the  soul,  those  uni- 
versal from  which  demonstration  consists.     For  the  universal, 
which  is  the  proper  object  of  science,  is  not  derived  from  par- 
ticulars, since  these  are  infinite,  and  every  induction  of  them 
must  be  limited  to  a  finite  number.     Hence  the  perception  of  the 
all  and  the  every  is  only  excited,  and  not  produced,  by  induc- 
tion." ^     In  other  words  the  category  of  totality  seems  to  be  a 
function  of  the  mind  that  is  aroused  or  excited  by  the  perception 
of  particular  things.     The  mind  makes  the  leap  from  the  part 
to  the  whole. 

In  another  place  Aristotle  tries  to  prove  the  inductive  propo- 
sition deductively,  that  is,  to  justify  the  inductive  leap  to  logic. 
He  bases  himself  on  the  thought  that  we  can  enumerate  all  the 
species  of  the  genus  which  occurs  in  our  conclusion.  Thus  we 
conclude  that  whatever  is  devoid  of  bile  is  longlived,  because 
every  man,  horse,  mule,  etc.,  is  longlived,  and  what  is  devoid  of 
bile  is  man,  horse,  mule,  etc.^  That  is,  only  so-called  perfect 
induction  is  capable  of  proof.^ 

The  thought  implied  by  Aristotle  is  that  what  is  true  of  the 

^Posterior  Analytics,  Bk.  II,  chap  xix. 

^Quoted  in  the  English  translation  of  the  Orffanoti,  Bohn's  library. 
''Prior  Analytics,  Bk.  II,   chap,  xxiii, 

6See  also,  Whately,   Logic;  Apelt,   Theorie  der   Induction;  Jevons,. 
Lessons  in  Logic;  Principles  of  Science ;  Veitch,  Institutes  of  Logic. 


151]        THE  PROCESS  OF  INDUCTIVE  INFERENCE  3 

species  is  true  of  the  genus,  that  the  particular  is  an  expression 
of  the  universal,  that  there  is  uniformity  in  the  world.  This  is 
really  the  fundamental  idea  of  his  whole  system  of  philosophy. 
The  particular  is  an  expression  of  the  universal,  of  the  form  or 
idea,  hence  what  is  true  of  the  particular  must  be  true  of  the 
universal.''' 

§  2.  Bacon,  too,  regards  induction  as  a  passage  from  the 
particular  to  the  general.  But  he  suggests  a  more  careful 
method  of  procedure.  "For  the  induction  which  proceeds  by 
simple  enumeration  is  childish,"  he  says;  "its  conclusions  are 
precarious,  and  exposed  to  peril  from  a  contradictory  instance; 
and  it  generally  decides  on  too  small  a  number  of  facts,  and  on 
those  only  which  are  at  hand.  But  the  induction  which  is  to  be 
available  for  the  discovery  and  demonstration  of  sciences  and 
arts,  must  analyze  nature  by  proper  rejections  and  exclusions; 
and  then  after  a  sufficient  number  of  negatives,  come  to  a  con- 
clusion on  the  affirmative  instances."  ^  He  also  condemns  hasty 
induction,  and  finds  fault  with  the  ancients  for  having  employed 
it.  "From  a  few  examples  and  particulars  (with  the  addition 
of  common  notions  and  perhaps  of  some  portion  of  the  received 
opinions  which  have  been  most  popular),  they  flew  at  once  to 
the  most  general  conclusions,  or  first  principles  of  science;  taking 
the  truth  of  these  as  fixed  and  immovable,  they  proceeded  by 
means  of  intermediate  propositions  to  educe  and  prove  from 
them  the  inferior  conclusions :  and  out  of  these  they  framed  the 
art."  ^  "There  are  and  can  be  only  two  ways  of  searching  into 
and  discovering  truth.     The  one  flies  from  the  senses  and  par- 

^See  Hegel's  Logih.    See  also,  Posterior  Analytics,  Bk.  I,  chap.  xxxi. 
^Novum  Organum,  Bk.   I,    cv.       Quotations    taken    from  the  Sped- 
ding,  Ellis,  and  Heath  edition  of  Bacon's  Works. 
^Nov.  Org.,  Bk.  I,  cxxv. 


4  UNIVERSITY  OF  MISSOURI  STUDIES  [152 

liculars  to  the  most  general  axioms,  and  from  these  principles, 
tlie  truth  of  which  it  takes  for  settled  and  immovable,  proceeds 
to  judgment  and  to  the  discovery  of  middle  axioms.  And  this 
way  is  now  in  fashion.  The  other  derives  axioms  from  the 
senses  and  particulars,  rising  by  a  gradual  and  unbroken  ascent, 
so  that  it  arrives  at  the  most  general  axioms  last  of  all.  This 
is  the  true  way,  but  as  yet  untried."  ^^ 

Bacon's  whole  aim  is  to  devise  a  method  that  will  yield  us 
general  propositions  of  greater  certainty  than  those  obtained  by 
the  method  of  simple  enumeration.  The  problem  is  to  find  the 
form  or  essence  of  things,  that  on  which  the  phenomenon  under 
consideration  depends.  The  form  of  anything  is  inherent  in 
each  individual  instance  in  which  the  thing  itself  is  inherent.^ ^ 
"The  investigation  of  Forms  proceeds  thus;  a  nature  being 
given,  we  must  first  of  all  have  a  muster  or  presentation  before 
the  understanding  of  all  known  instances  which  agree  in  the 
same  nature,  though  in  substance  the  most  unlike."  ^^     Such  a 

^^Nov.  Org.,  Bk.  I,  xix. 

"^^Nov.  Org.,  Bk.  II,  xx;  Bk.  II,  ii:  "For  though  in  nature 
nothing  exists  besides  individual  bodies,  performing  pure  individual 
acts  according  to  a  fixed  law,  yet  in  philosophy  this  very  law,  and  the 
investigation,  discovery,  and  explanation  of  it,  is  the  foundation  as  well 
of  knowledge  as  of  operation.  And  it  is  this  law,  with  its  clauses,  that 
I  mean  when  I  speak  of  Fortns;  a  name  which  I  the  rather  adopt  be- 
cause it  has  grown  into  use  and  become  familiar."  Bk.  II,  iv: 
"For  the  Form  of  a  nature  is  such,  that  given  the  Form  the  nature  infal- 
libly follows.  Therefore  it  is  always  present  when  the  nature  is  present, 
and  universally  implies  it,  and  is  constantly  inherent  in  it,"  etc.  Bk.  II, 
xvii:  "For  when  I  speak  of  Forms,  I  mean  nothing  more  than 
those  laws  and  determinations  of  absolute  actuality,  which  govern  and 
constitute  any  simple  nature,  as  heat,  light,  weight,  in  every  kind  of 
matter  and  subject  that  is  susceptible  of  them."  See  also,  Bk.  II, 
iii,  v,  xiii,  xv,  xvi. 

^Nov.  Org.,  Bk.  II,  xi. 


^53]  ^^^  PROCESS  OF  INDUCTIVE  INFERENCE  5 

list  is  called  the  table  of  essence  or  presence.  "Secondly,  we 
must  make  a  presentation  to  the  understanding  of  instances  in 
which  the  given  nature  is  wanting;  because  the  Form,  as  stated 
above,  ought  no  less  to  be  absent  when  the  given  nature  is 
absent,  than  present  when  it  is  present."  ^^  This  is  the  table 
of  deviation  or  of  absence  in  proximity.  "Thirdly,  we  must 
make  a  presentation  to  the  understanding  of  instances  in  which 
the  nature  under  inquiry  is  found  in  different  degrees,  more  or 
less."  ^^  This  is  the  table  of  degrees  or  of  comparison.  When 
all  this  has  been  done  induction  itself  is  brought  into  action. 
"The  first  work  therefore  of  true  induction  (as  far  as  regards 
the  discovery  of  Forms)  is  the  rejection  or  exclusion  of  the 
several  natures  which  are  not  found  in  some  instance  where  the 
given  nature  is  present,  or  are  found  in  some  instance  where 
the  given  nature  is  absent,  or  are  found  to  increase  in  some 
instance  when  the  given  nature  decreases,  or  to  decrease  when 
the  given  nature  increases.  Then  indeed  after  the  rejection  and 
exclusion  has  been  duly  made,  there  will  remain  at  the  bottom, 
all  light  opinions  vanishing  into  smoke,  a  Form  affirmative,  solid 
and  true  and  well  defined."  i» 

It  is  apparently  the  business  of  the  investigator  to  collect 
a  number  of  diiYerent  cases  in  which  the  phenomenon  to  be 
studied  is  present.  Then  he  must  collect  cases  in  which  it  is 
absent,  and  also  cases  in  which  it  varies.  That  which  is  always 
present  when  the  phenomenon  is  present,  and  absent  when  the 
phenomenon  is  absent,  and  which  varies  with  the  phenomenon, 
is  the  sought-for  form. 

It  is  clear.  Bacon  unconsciously  bases  himself  upon  the  prin- 
ciple that  there  is  a  necessary  connection  between  things,  and 

^Wov.  Org-.,  Bk.  II,  xii. 
^*JVov.  Org.,  Bk.  II,  xiii. 
'^^Nov.  Org.,  Bk.  II,  xvi. 


6  UNIVERSITV  OP^   MISSOURI  STUDIES  [154 

that  it  is  the  business  of  true  induction  to  find  this  connection. 
He  reallv  assumes  that  there  is  uniformity  in  nature,  that  things 
are  so  connected  that  when  one  appears  the  other  will  appear 
also.  This  principle  he  does  not  attempt  to  justify;  indeed,  as 
we  have  already  said,  he  is  not  conscious  of  it  at  all.  Since, 
however,  he  rejects  the  theory  of  innate  ideas,  and  accepts 
empiricism,  it  is  safe  to  say  that  he  would  have  explained  this 
principle  as  a  product  of  experience  after  the  fashion  of  Mill. 

§  3.  John  Stuart  Mill  ^^  defines  induction  as  "that  opera- 
tion of  the  mind,  by  which  we  infer  that  which  we  know  to  be 
true  in  a  particular  case  or  cases,  will  be  true  in  all  cases  which 
resemble  the  former  in  certain  assignable  respects.  In  other  words, 
induction  is  the  process  by  which  we  conclude  that  what  is  true 
of  certain  individuals  of  a  class  is  true  of  the  whole  class,  or  that 
what  is  true  at  certain  times  will  be  true  in  similar  circumstances 
at  all  times."  1"  So-called  perfect  induction  is  not  induction  at 
all.  Nor  are  those  cases  in  mathematics  induction,  in  which  the 
conclusion  is  a  mere  summing  up  of  what  was  asserted  in  the 
various  propositions  from  which  it  is  drawn.  Nor  is  it  induc- 
tion to  piece  detached  fragments  together  (the  so-called  colliga- 
tion of  facts). ^^ 

Mill  finds  the  ground  of  induction-  in  the  principle  of  the 
uniformity  of  nature.^^ 

"The  proposition  that  the  course  of  nature  is  uniform,  is 
the  fundamental  principle,  or  general  axiom,  of  induction.  But 
it  would  be  a  great  error  to  offer  this  large  generalization  as  any 
explanation  of  the  inductive  process.     It  is  itself  an  instance  of 

^M  Sysiem  of  Logic,  Bk.  III. 

^''Log-ic,  Bk.  Ill,  chap,  ii,  §1.     See  also,  chap,  i,  §2. 

^^Logic,  Bk.  Ill,  chap,  ii,  §§3,4. 

^^Logic,  Bk.  Ill,  chap.  iii. 


155]  THE  PROCESS  OF  INDUCTIVE  INFERENCE  7 

induction,  and  induction  by  no  means  of  the  most  obvious  kind. 
Far  from  being  the  first  induction  we  make,  it  is  one  of  the  last, 
or  at  all  events  one  of  those  which  are  latest  in  attaining  strict 
philosophical  accuracy." 

This  great  generalization,  however,  is  itself  founded  on 
prior  generalizations.  "The  obscurer  laws  of  nature  were  dis- 
covered by  means  of  it,  but  the  more  obvious  ones  must  have 
been  understood  and  assented  to  as  general  truths  before  it  was 
ever  heard  of.  We  should  never  have  thought  of  affirming  that 
all  phenomena  take  place  according  to  general  laws,  if  we  had  not 
first  arrived,  in  the  case  of  a  great  multitude  of  phenomena,  at 
some  knowledge  of  the  laws  themselves ;  which  could  be  done  no 
otherwise  than  by  induction."  ^o  This  principle  is  our  warrant 
for  all  the  other  inductions  in  the  sense  in  which  the  general 
propositions  which  we  place  at  the  head  of  our  reasonings  ever 
really  contribute  to  their  validity.  The  major  premise  of  a  syl- 
logism does  not  prove  the  conclusion,  but  is  a  necessary  condition 
of  its  being  proved.  Every  induction  may  be  thrown  into  the 
form  of  a  syllogism,  by  supplying  a  major  premise.  "If  this  be 
actually  done,  the  principle  which  we  are  now  considering,  that 
of  the  uniformity  of  the  course  of  nature,  will  appear  as  the  ul- 
timate major  premise  of  all  inductions,  and  will,  therefore  stand 
to  all  inductions  in  the  relation  in  which  *  *  *  the  major  propo- 
sition of  a  syllogism  always  stands  to  the  conclusion;  not 
contributing  at  all  to  prove  it,  but  being  a  necessary  con- 
dition of  its  being  proved;  since  no  conclusion  is  proved, 
for  which  there  can  not  be  found  a  true  major  premise." 
"The  real  proof  that  what  is  true  of  John,  Peter,  etc.,  is  true 
of  all  mankind,  can  only  be,  that  a  different  suppos- 
ition would  be  inconsistent  with  the  uniformity  which  we 
know  to  exist  in  the  course  of  nature.  Whether  there 
would  be  this  inconsistency  or  not,  may  be  a  matter  of  long  and 
"^Logic,  Bk.  Ill,  chap,  iii,  §1. 


S  UNIVERSITY  OF   MISSOURI  STUDIES  [156 

delicate  inquiry;  but  unless  there  would,  we  have  no  sufficient 
ground  for  the  major  of  the  inductive  syllogism.  It  hence  ap- 
pears, that  if  we  throw  the  whole  course  of  any  inductive  argu- 
ment into  a  series  of  syllogisms,  we  shall  arrive  by  more  or  fewer 
steps  at  the  ultimate  syllogism,  which  will  have  for  its  major 
premise  the  principle,  or  axiom,  of  the  uniformity  of  the  course 
of  nature."  21 

The  validity  of  all  the  Inductive  Methods  (Agreement,  Dif- 
ference, Joint  Method,  etc.)  depends  on  the  assumption  that 
every  event,  or  the  beginning  of  every  phenomenon,  must  have 
some  cause ;  some  antecedent,  on  the  existence  of  which  it  is  in- 
varibly  and  unconditionally  consequent.  22  This  assumption  is 
itself  an  instance  of  induction.  We  arrive  at  this  universal  law, 
by  generalization  from  many  laws  of  inferior  generality.  As, 
however,  all  rigorous  processes  of  induction  presuppose  the  gen- 
eral uniformity,  our  knowledge  of  the  particular  uniformities 
from  which  it  was  first  inferred  was  not,  of  course,  derived  from 
rigorous  induction,  but  by  the  loose  and  uncertain  mode  of  in- 
duction per  enumerationem  simplicem;  and  the  law  of  universal 
causation,  being  collected  from  results  so  obtained,  can  not  it- 
self rest  on  any  better  foundation.  Induction  per  enumera- 
tionem simplicem  is,  however,  not  only  not  necessarily  an  illicit 
logical  process,  but  is  in  reality  the  only  kind  of  induction  pos- 

"^^Logic,  Bk.  Ill,  chap,  iii,  §1. 

^Logic,  Bk.  Ill,  chap,  xxi,  §i.  See  also,  chap,  v,  §2:  "The  Law  of 
Causation,  the  recognition  of  which  is  the  main  pillar  of  inductive  sci- 
ence, is  but  the  familiar  truth,  that  invariability  of  succession  is  found 
by  observation  to  obtain  between  every  fact  in  nature  and  some  other 
fact  which  has  preceded  it."  Section  6:  But,  "invariable  sequence  is 
not  causation,  unless  the  sequence,  besides  being  invariable,  is  uncon- 
ditional." "We  may  define,  therefore,  the  cause  of  a  phenomenon,  to 
be  the  antecedent,  or  the  concurrence  of  antecedents,  on  which  it  is  in- 
variably and  iinconditionally  consequent." 


157]  THE  PROCESS  OF  INDUCTIVE  INFERENCE  9 

sible.23  The  precariousness  of  this  process  is  in  inverse  ratio 
to  the  largeness  of  the  generalization.  It  is  for  this  reason  that 
the  most  universal  class  of  truths,  the  law  of  causation,  for  in- 
stance, and  the  principles  of  number  and  of  geometry,  are  duly 
and  satisfactorily  proved  by  that  method  alone,  nor  are  they 
susceptible  of  any  other  proof.^^  The  assertion,  that  our  induc- 
tive processes  assume  the  law  of  causation,  while  the  law  of  caus- 
ation is  itself  a  case  of  induction,  is  a  paradox,  only  on  the  old 
theory  of  reasoning,  which  supposes  the  universal  truth,  or  ma- 
jor premise,  in  a  ratiocination,  to  be  the  real  proof  of  the  partic- 
ular truths  which  are  ostensibly  inferred  from  it.  According 
to  Mill's  doctrine,  however,  "the  major  premise  is  not  the  proof 
of  the  conclusion,  but  is  itself  proved,  along  with  the  conclusion 
from  the  same  evidence.  'All  men  are  mortal'  is  not  the  proof 
that  Lord  Palmerston  is  mortal ;  but  our  past  experience  of  mor- 
tality authorizes  us  to  infer  both  the  general  truth  and  the  partic- 
ular fact,  and  the  one  with  exactly  the  same  degree  of  assurance 
as  the  other.  The  mortality  of  Lord  Palmerston  is  not  an  in- 
ference from  the  mortality  of  all  men,  but  from  the  experience 
which  proves  the  mortality  of  all  men ;  and  is  a  correct  inference 
from  experience,  if  that  general  truth  is  so  too.     This  relation 

^Log-ic,  Bk.  Ill,  chap,  xxi,  §2:  "Is  there  not  then  an  inconsistency 
in  contrasting  the  looseness  of  one  method  with  the  rigidity  of  another, 
when  that  other  is  indebted  to  the  looser  method  for  its  own  foundation  ? 
The  inconsistency,  however,  is  only  apparent.  Assuredly,  if  induction 
by  simple  enumeration  were  an  invalid  process,  no  process  founded  on 
it  could  be  valid;  just  as  no  reliance  could  be  placed  on  telescopes,  if  we 
could  not  trust  our  eyes.  But  though  a  valid  process,  it  is  a  fallible 
one,  and  fallible  in  very  different  degrees;  if,  therefore,  we  can  substi- 
tute for  the  more  fallible  forms  of  the  process,  an  operation  founded  on 
the  same  process  in  a  less  fallible  form,  we  shall  have  effected  a  very 
material  imorovement.     And  this  is  what  scientific  induction  does." 

"^Logic,  Bk.  Ill,  chap,  xxi,  §§2,4. 


lO  UNIVERSITY  OF  MISSOURI  STUDIES  [158 

between  our  general  beliefs  and  their  particular  applications 
holds  equally  true  in  the  more  comprehensive  case  which  we  are 
now  discussing.  Any  new  fact  of  causation  inferred  by  induc- 
tion is  rightly  inferred,  if  no  other  objection  can  be  made  to  the 
inference  than  can  be  made  to  the  general  truth  that  every  event 
has  a  cause.  The  utmost  certainty  which  can  be  given  to  a  con- 
clusion arrived  at  in  the  way  of  inference,  stops  at  this  point. 
When  we  have  ascertained  that  the  particular  conclusion  must 
stand  or  fall  with  the  general  uniformity  of  the  laws  of  nature — 
that  it  is  liable  to  no  doubt  except  the  doubt  whether  every  event 
has  a  cause — we  have  done  all  that  can  be  done  for  it."  In  mat- 
ters of  evidence  as  in  all  other  human  things,  we  neither  require, 
nor  can  attain,  the  absolute.  "Whatever  has  been  found  true  in 
innumerable  instances,  and  never  found  to  be  false  after  due  ex- 
amination in  many,  we  are  safe  in  acting  on  as  universal  provis- 
ionally, until  an  undoubted  exception  appears;  provided  the  na- 
ture of  the  case  be  such  that  a  real  exception  could  scarcely  have 
escaped  notice.  When  every  phenomenon  that  we  ever  knew 
sufficiently  well  to  be  able  to  answer  the  question,  had  a  cause  on 
which  it  was  invariably  consequent,  it  was  more  rational  to  sup- 
pose that  our  inability  to  assign  the  causes  of  other  phenomena 
arose  from  our  ignorance,  than  that  there  were  phenomena  which 
w-ere  uncaused,  and  which  happened  to  be  exactly  those  which 
we  had  hitherto  had  no  sufficient  opportunity  of  studying."  ^^ 

"^Logic,  Bk.  Ill,  chap,  xxi,  §4.  Mill  goes  on  to  say:  "It  must,  at 
the  same  time,  be  remarked,  that  the  reasons  for  this  reliance  do  not 
hold  in  circumstances  unknown  to  us,  and  beyond  the  possible  range  of 
our  experience.  In  distant  parts  of  the  stellar  regions,  where  the  phe- 
nomena may  be  entirely  unlike  those  with  which  we  are  acquainted,  it 
would  be  folly  to  affirm  confidently  that  this  general  law  prevails,  any 
more  than  those  special  ones  which  we  have  found  to  hold  universally  on 
our  own  planet.  The  uniformity  in  the  succession  of  events,  otherwise 
called  the  law  of  causation,  must  be  received  not  as  a  law  of  the  universe, 


159]  THE  PROCESS  OF  INDUCTIVE  INFERENCE  II 

Mill  too,  we  see,  grounds  induction  on  the  proposition  that 
things  are  connected  in  such  a  way  that  when  one  appears  the 
other  will  appear  also.  This  proposition  itself  is  a  product  of 
experience,  the  result  of  loose  induction.^^  But  we  are  satisfied 
with  this  loose  induction  on  account  of  the  great  number  of  par- 
ticular cases  observed  by  us  in  which  we  experience  causality. 
Moreover,  the  particular  case  is  not  proved  by  the  general  prop- 
osition at  all ;  the  general  proposition  is  proved  by  the  particular 
cases.  Hence,  everything  is  ultimately  reduced  by  Mill  to  induc- 
tion; induction  is  the  only  possible  process  of  inference;  deduc- 
tion is  not  inference  at  all,  but  a  mere  deciphering  of  our  notes. 
"All  inference  is  from  particulars  to  particulars;  general 
propositions  are  merely  registers  of  such  inferences  already  made 
and  short  formulae  for  making  more.  The  major  premise  of 
a  syllogism,  consequently,  is  a  formula  of  this  description;  and 

but  of  that  portion  of  it  only  which  is  within  the  range  of  our  means  of 
sure  observation,  with  a  reasonable  degree  of  extension  to  adjacent 
cases.  To  extend  it  further  is  to  make  a  supposition  without  evidence, 
and  to  which  in  the  absence  of  any  ground  from  experience  for  estimat- 
ing its  degree  of  probability,  it  would  be  idle  to  attempt  to  assign  any." 
^Logic,  Bk.  Ill,  chap,  xxi,  §1 :  Some  metaphysicians  affirm  "that 
the  universality  of  causation  is  a  truth  which  we  can  not  help  believing; 
that  the  belief  in  it  is  an  instinct,  one  of  the  laws  of  our  believing  fac- 
ulty." But  "belief  is  not  truth,  and  does  not  dispense  with  the  neces- 
sity of  truth."  "Now  a  mere  disposition  to  believe,  even  if  supposed 
instinctive,  is  no  guarantee  for  the  truth  of  the  thing  believed.  If,  in- 
deed, the  belief  ever  amounted  to  an  irresistible  necessity,  there  would 
then  be  no  use  in  appealing  from  it,  because  there  would  be  no  possibil- 
ity of  uttering  it.  But  even  then  the  truth  of  the  belief  would  not  fol- 
low; it  would  only  follow  that  mankind  were  under  a  permanent  neces- 
sity of  believing  what  might  possiblj'  not  be  true.  *  *  *  3yt  j^  fact 
there  is  no  such  permanent  necessity.  There  is  not  one  of  these  sup- 
posed instinctive  beliefs  which  is  really  inevitable.  *  *  *  It  is  not 
true,  as  a  matter  of  fact,  that  mankind  have  always  believed  that  all  the 
succession  of  events  were  uniform  and  according  to  fixed  laws.     *     *     * 


12 


UNIVERSITY  OF  MISSOURI  STUDIES  [l6o 


tlio  conclusion  is  not  an  inference  drawn  from  the  formula,  but 
an  inference  drawn  according  to  the  formula;  the  real  logical  an- 
tecedent or  premise  being  the  particular  facts  from  which  the 
general  proposition  was  collected  by  induction.  Those  facts, 
and  the  individual  instances  which  supplied  them,  may  have  been 
forgotten;  but  a  record  remains,  not  indeed  descriptive  of  the 
facts  themselves,  but  showing  how  those  cases  may  be  distin- 
guished, respecting  which,  the  facts,  when  known,  were  consid- 
ered to  warrant  a  given  inference.  According  to  the  indications 
of  this  record  we  draw  our  conclusion:  which  is,  to  all  intents 
and  purposes,  a  conclusion  from  the  forgotten  facts.  For  this 
it  is  essential  that  we  should  read  the  records  correctly :  and  the 
rules  of  the  syllogism  are  a  set  of  precautions  to  insure  our  doing 
so."  "The  proposition.  All  men  are  mortal  (for  instance)  shows 
that  we  have  had  experience  from  which  we  thought  it  followed 

Even  now  a  full  half  of  the  philosophical  world,  including  the  very  same 
metaphysicians  who  contend  most  for  the  instinctive  character  of  the 
belief  in  uniformity,  consider  one  important  class  of  phenomena,  voli- 
tions, to  be  an  exception  to  the  uniformity,  and  not  governed  by  a  fixed 
law."  Chap,  xxi,  §3,  Note:  "Dr.  McCosh  maintains  that  the  uniform- 
ity of  the  course  of  nature  is  a  different  thing  from  the  law  of  causation, 
and  while  he  allows  that  the  former  is  only  proved  by  a  long  continu- 
ance of  experience,  and  that  it  is  not  inconceivable  nor  necessarily  in- 
credible that  there  may  be  worlds  in  which  it  does  not  prevail,  he  con- 
siders the  law  of  causation  to  be  known  intuitively.  There  is,  however, 
no  other  uniformity  in  the  events  of  nature  than  that  which  arises  from 
the  law  of  causation;  so  long,  therefore,  as  there  remained  any  doubt 
that  the  course  of  nature  was  uniform  throughout,  at  least  when  not 
modified  by  the  intervention  of  a  new  (supernatural)  cause,  a  doubt 
was  necessarily  implied,  not  indeed  of  the  reality  of  causation,  but  of  its 
universality.  If  the  uniformity  of  the  course  of  nature  has  any  excep- 
tions— if  any  events  succeed  one  another  without  fixed  laws — to  the  ex- 
tent the  law  of  causation  fails;  there  are  events  which  do  not  depend  on 
causes." 


l6l]  THE  PROCESS  OF  INDUCTIVE  INFERENCE  I3 

that  the  attributes  connoted  by  the  term  man,  are  a  mark  of  mor- 
tality. But  when  we  conclude  that  the  Duke  of  Wellington  is 
mortal,  we  do  not  infer  this  from  the  memorandum,  but  from  the 
former  experience.  All  that  we  infer  from  the  memorandum 
is  our  own  previous  belief,  (or  that  of  those  who  transmitted  to 
us  the  proposition),  concerning  the  inferences  which  that  former 
experience  would  warrant."  2" 

§  4.  According  to  Jevons  ^s  it  cannot  be  said  that  the  in- 
ductive process  is  of  greater  importance  than  the  deductive  pro- 
cess, because  the  latter  process  is  absolutely  essential  to  the 
former.  Each  is  the  complement  and  counterpart  of  the  other. 
Induction  is  in  fact  the  inverse  operation  of  deduction,  and  cannot 
be  conceived  to  exist  without  the  corresponding  operation.  In 
deduction  we  deduce  from  certain  conditions,  laws,  or  identities 
governing  the  combinations  of  qualities,  the  nature  of  the  com- 
binations agreeing  with  those  conditions.  Our  work  is  to  unfold 
what  is  contained  in  any  statements,  and  the  process  is  one  of 
synthesis.  In  induction  all  is  inverted.  The  truths  to  be  ascer- 
tained are  more  general  than  the  data  from  which  they  are 
drawn.  The  process  by  which  they  are  reached  is  analytical, 
and  consists  in  separating  the  complex  combinations  in  which 
natural  phenomena  are  presented  to  us,  and  determining  the  re- 
lations of  separate  qualities. 

Given  events  obeying  certain  unknown  laws,  we  have  to  dis- 
cover the  laws  obeyed.  Instead  of  the  comparatively  easy  task 
of  finding  what  effects  will  follow  from  a  given  law,  the  effects 
are  now  given  and  the  law  is  required.  We  have  to  interpret  the 
will   by   which   the   conditions   of   creation   were   laid   down.^* 

"^Logic,  Bk.  II,  chap,  iii,  §4. 

"^Elementary  Lessons  ift  Logic;  Principles  of  Science. 

^Principles  of  Scie?ice,  chap.  vii. 


I  .  UNIVEKSITV  OK  MISSOURI  STUDIES  [162 

Being  ill  possession  of  certain  particular  facts  or  events  ex- 
pressed in  propositions,  we  imagine  some  more  general  propo- 
sition expressing  the  existence  of  a  law  or  cause ;  and,  deducing 
the  particular  results  of  that  supposed  general  proposition,  we 
observe  whether  they  agree  with  the  facts  in  question.  Hypoth- 
esis is  thus  always  employed  consciously  or  unconsciously. 
Thus  there  are  but  three  steps  in  the  process  of  induction :  ( i ) 
Framing  some  hypothesis  as  to  the  character  of  the  general  law. 
(2)  Deducing  consequences  from  that  law.  (3)  Observing 
whetlier  the  consequences  agree  with  the  particular  facts  under 
consideration.^" 


^Principles  of  Science,  chap.  xii.  Here  Jevons  seems  to  identify  in 
duction  with  scientific  method  in  general,  which  is  really  a  combination 
of  induction  and  deduction.  But  there  are  passages  in  his  Principles  of 
Science,  and  particularly  in  his  elementary  work,  which  do  not  appear 
to  be  consistent  with  this  interpretation.  In  chapter  xi  of  the  first-named 
book,  for  example,  he  says:  "We  must  carefully  avoid  confusing  to- 
gether inductive  investigations  which  terminate  in  the  establishment  of 
general  laws,  and  those  which  seem  to  lead  to  the  knowledge  of  particu- 
lar events.  That  process  only  can  be  called  induction  which  gives  gen- 
eral laws,  and  it  is  by  the  subsequent  employment  of  deduction  that  we 
anticipate  particular  events.  If  the  observation  of  a  number  of  cases 
shows  that  alloys  of  metals  fuse  at  lower  temperatures  than  their  con- 
stituent metals,  I  may  with  more  or  less  probability  draw  a  general  in- 
ference to  that  effect,  and  may  thence  deductively  ascertain  the  proba- 
bility that  the  next  alloy  examined  will  fuse  at  a  lower  temperature  than 
its  constituents."  "I  hold  that  in  all  cases  of  inductive  inference  we 
must  invent  hypotheses,  until  we  fall  upon  some  hypothesis  which  yields 
deductive  results  in  accordance  with  experience.  Such  accordance  ren- 
ders the  chosen  hypothesis  more  or  less  probable,  and  we  may  then 
deduce,  with  some  degree  of  likelihood,  the  nature  of  our  future  ex- 
perience, on  the  assumption  that  no  arbitrary  change  takes  place  in  the 
conditions  of  nature."  See  also,  Lessons  in  Logic,  Lesson  xxx,  pp.  258f, 
quoted  in  the  second  part  of  this  paper,  page  35. 


[63 J  THE  PROCESS  OF  INDUCTIVE  INFERENCE  1 5 

But  the  results  of  imperfect  induction  are  never  more  than 
probable.  "It  is  a  question  of  profound  difificulty  on  what 
grounds  we  are  warranted  in  inferring  the  future  from  the  pres- 
ent, or  the  nature  of  undiscovered  objects  from  those  which  we 
have  examined  with  our  senses.  We  pass  from  Perfect  to  Im- 
perfect Induction  when  once  we  allow  our  conclusion  to  apply, 
at  all  events  apparently,  beyond  the  data  on  which  it  was 
founded.  In  making  such  a  step  we  seem  to  gain  a  net  addition 
to  our  knowledge;  for  we  learn  the  nature  of  what  was  un- 
known. We  reap  where  we  have  never  sown.  We  appear  to 
possess  the  divine  power  of  creating  knowledge,  and  reaching 
with  out  mental  arms  far  beyond  the  sphere  of  our  own  observa- 
tion. Of  imperfect  induction  itself,  I  venture  to  assert  that  it 
never  makes  any  real  addition  to  our  knowledge,  in  the  meaning 
of  the  expression  sometimes  accepted.  As  in  other  cases  of  in- 
ference, it  merely  unfolds  the  information  contained  in  past  ob- 
servations; it  merely  renders  explicit  what  was  impHcit  in  pre- 
vious experience.  It  transmutes,  but  certainly  does  not  create 
knowledge."  The  results  of  imperfect  induction,  however  well 
authenticated  and  verified,  are  never  more  than  probable.  "We 
never  can  be  sure  that  the  future  will  be  as  the  present.  We 
hang  ever  upon  the  will  of  the  Creator :  and  it  is  only  as  far  as 
He  has  created  two  things  alike,  or  maintains  the  framework  of 
the  world  unchanged  from  moment  to  moment,  that  our  most 
careful  inferences  can  be  fulfilled.  All  predictions,  all  inferences 
which  reach  beyond  their  data,  are  purely  hypothetical,  and  pro- 
ceed on  the  assumption  that  new  events  will  conform  to  the  con- 
ditions detected  in  our  observation  of  past  events.  No  experience 
of  finite  duration  can  give  an  exhaustive  knowledge  of  the  forces 
which  are  in  ooeration.  There  is  thus  a  double  uncertainty ;  even 
supposing  the  Universe  as  a  whole  to  proceed  unchanged,  we  do 
not  really  know  the  Universe  as  a  whole.  We  know  only  a  point 


I  6  UNIVERSITY  OF  MISSOURI  STUDIES  [164 

in  its  infinite  extent,  and  a  moment  in  its  infinite  duration.  We 
cannot  be  sure,  then,  that  our  observations  have  not  escaped 
some  fact,  which  will  cause  the  future  to  be  apparently  different 
from  the  past ;  nor  can  we  be  sure  that  the  future  really  will  be 
the  outcome  of  the  past.  We  proceed,  then,  in  all  our  inferences 
to  the  unexamined  objects  and  times  on  the  assumptions  which 
are  always  uncertain :  ( i )  that  our  past  observation  gives  us  a 
complete  knowledge  of  what  exists;  (2)  that  the  conditions  of 
things  which  did  exist  will  continue  to  be  the  conditions  which 
will  exist."  31 

Jevons  identifies  induction  with  specific  method  in  general. 
But  he  also  bases  it  on  the  principle  that  there  are  uniform  con- 
nections in  nature,  and  regards  this  principle  as  a  product  of  ex- 
perience. 

§5.  According  to  Sigwart,  ^^  ^i^g  logical  justification 
of  the  inductive  process,  that  is,  the  attainment  of  universal  prop- 

^^Prtttciples  of  Science,  chap.  vii.  Compare  chap,  xi:  "We  can  only 
argue  from  the  past  to  the  future,  on  the  general  principle  set  forth  in 
this  work,  that  what  is  true  of  a  thing  will  be  true  of  the  like.  So  far 
then  as  one  object  or  event  differs  from  another,  all  inference  is  impos- 
sible, particulars  as  particulars  can  no  more  make  an  inference  than 
grains  of  sand  can  make  a  rope.  We  must  always  rise  to  something 
which  is  general  or  same  in  the  cases,  and  assuming  that  sameness  to  be 
extended  to  new  cases  we  learn  their  nature."  "There  is  no  reason  in 
the  nature  of  things,  so  far  as  known  to  us,  why  yellow  color,  ductility, 
high  specific  gravity,  and  incorrodibility,  should  always  be  associated 
together,  and  in  other  cases,  if  not  in  this,  men's  expectations  have  been 
deceived.  Our  inferences,  therefore,  always  retain  more  or  less  of  a 
hypothetical  character,  and  are  so  far  open  to  doubt.  Only  in  so  far  as 
our  induction  approximates  to  the  character  of  perfect  induction,  does 
it  approximate  to  certainty."  See  also,  on  this  point,  Hamilton,  Dis- 
cussions; VtSXch.,  Institutes  of  Logic;  Benno  Erdmann,  Z^o^//^. 

^Logic,  vol.  II,  chap.  v.       The  quotations   are   taken   from    Helen 
Dendy's  English  translation. 


165]        THE  PROCESS  OF  INDUCTIVE  INFERENCE  1*J 

ositions  from  particular  judgments  of  perception,  rests  upon  the 
fact  that  it  is  an  inevitable  postulate  of  our  effort  after  knowl- 
edge that  the  given  is  necessary,  and  can  be  known  as  proceeding 
from  its  grounds  according  to  universal  laws.^s  Every  inductive 
inference  contains  a  universal  principle.  If  it  is  to  be  an  infer- 
ence and  not  merely  an  association  of  merely  subjective  validity, 
the  transition  from  the  empirically  universal  judgment  all  known 
A's  are  B's  to  the  unconditionally  universal  all  that  is  A  is  B, 
can  only  be  made  by  means  of  a  universal  major  premise;  and 
that  only  upon  condition  of  this  being  true  are  we  justified  in  in- 
ferring from  the  particular  known  A's  to  the  still  unknown  A's. 
But  then  the  universal  major  premise  cannot  be  obtained  simply 
by  means  of  a  summation  of  facts,  for  this  by  itself  can  yield 
no  more  than  it  says,  that  is,  a  certain  number  of  cases  A  was  B 
and  as  a  pure  matter  of  fact  contains  no  reason  for  passing  be- 
yond these  A's  to  other  A's. 

The  universal  major  premise  must  have  some  other  origin 
than  in  previously  observed  facts,  and  our  right  to  make  use  of  it 
must  have  some  other  ground  than  the  narration  of  cases 
which  have  been  observed  so  far.^^  We  shall  never  find  in  the 
given  a  sufficient  ground  to  yield  us  the  conviction  that  because 
so  many  perceived  A's  have  without  exception  the  attribute  B, 
or  because  event  B  has  followed  so  many  times  upon  circum- 
stance A,  therefore  it  must  necessarily  be  so.  ''The  innumerable 
exceptions  by  which  many  attempted  generalizations  of 
this  kind  are  met  do  as  a  matter  of  fact,  refute,  even 
to  superfluity,  the  assumption  that  a  universal  law  can  be 
derived  with  infallible  certainty  from  similar  cases,  however 
great  their  number.     For  a  long  time  it  is  for  most  Europeans 

^Logic,  vol.  II,  chap,  v,  §93. 
^Logic,  vol.  II,  chap,  v,  §93,  8. 
(-2) 


iS  UNIVERSITY  OF  MISSOURI  STUDIES  [l66 

a  good  induction  that  all  men  are  white;  it  is  a  good  induction 
that  all  men  have  five  fingers;  for  thousands  of  years  it  was  a 
srood  induction  that  all  metals  are  heavier  than  water."  ^s 

The  universal  proposition  by  which  we  are  guided  in  our 
mental  elaboration  of  the  particular  propositions  given  by  per- 
ception is  that  the  given  is  necessary;  and  since  necessity  sig- 
nifies for  us  the  same  as  the  invariable  and  universal  connection 
of  a  ground  with  a  consequence,  we  get  as  the  postulate  of  our 
search  for  knowledge  that  every  particular  perception  is  an  in- 
stance of  a  general  rule,  a  conclusion  which  follows  from  subor- 
dination to  a  universal  major  premise.  This  presupposition  has 
reference  both  to  the  co-existence  of  the  permanent  attributes 
which  we  find  in  a  particular  object,  and  to  the  connection  be- 
tween the  changes  in  the  same  or  different  objects;  the  concepts 
of  things  in  which  we  synthesize  certain  perceptible  attributes 
at  first  as  subjective  images,  have  objective  significance  just  in 
so  far  as  the  connection  is  necessary,  and  there  is  a  general  rule 
according  to  which  these  attributes  exist  together  in  the  partic- 
ular case;  the  particular  event  is  necessary  when  it  happens  ac- 
cording to  a  rule  which  prescribes  that  under  certain  conditions 
a  certain  change  will  take  place.  Hence  it  follows  that  we  are 
forced  by  the  nature  of  knowledge  to  apprehend  all  particular 
objects  and  facts  with  which  observation  presents  us  as  instances 
in  which  a  universal  rule  expresses  itself ;  the  problem  of  induc- 
tion is  to  find  this  universal  rule,  and  to  formulate  it  in  such  a 
way  that  the  given  shall  everywhere  correspond  to  it. 
"In  other  words,  we  are  dealing  with  a  process  of  reduction, 
which  constructs  the  premises  from  which  the  particular  percep- 
tion follows  with  syllogistic  necessity,  whether  it  expresses  the 
co-existence  of  attributes  in  a  thing,  or  a  change,  or  the  succes- 
sion of  different  changes ;  and  the  problem  is  to  determine  these 

"^Logtc,  vol.  II,  chap,  v,  §93,   11. 


167]  THE  PROCESS  OF  INDUCTIVE  INFERENCE  I9 

major  premises  in  such  a  way  that  they  may  be  in  harmony  with 
all  the  perceptions  known  to  us."  ^^ 

From  this  it  follows  in  the  first  place  that  the  propositions 
gained  by  induction  are  neyer  proved  in  the  strict  sense,  but  from 
a  logical  point  of  view  are  only  hypotheses;  further  that  the 
fundamental  principles  even  of  induction  are  based  upon  the 
rules  of  the  syllogism,  by  which  it  is  determined  whether  the 
premises  assumed  lead  necessarily  to  the  conclusion.  If  a  per- 
ception does  not  agree  with  what  is  at  first  the  assumed  hypothe- 
sis of  a  universal  proposition,  then,  assuming  the  process  of  in- 
ference to  be  correct,  one  of  the  premises  is  necessarily  false; 
but  the  most  comprehensive  agreement  of  the  hypothesis  with  the 
facts  can  never  show  it  to  be  necessarily  true,  it  can  at  most 
make  it  probable.  When,  however,  any  one  hypothesis  breaks 
down  because  the  inferred  universal  proposition  is  opposed  by 
exceptions,  our  universal  presupposition  that  the  given  is  neces- 
sary is  not  on  that  account  destroyed;  it  is  only  the  special  as- 
sumption with  reference  to  the  necessary  connection  between  a 
special  ground  and  a  special  consequence  which  fails.^''' 

Induction  is  a  process  of  finding  universal  major  proposi- 
tions when  the  conclusions  are  given, — a  reduction  and  therefore 
the  reverse  process  of  the  syllogistic  deduction  from  given  major 
propositions.  All  induction  consists  in  framing  hypothetically 
universal  propositions  and  comparing  their  consequences  with 
the  given.  ^* 

Sigwart,  like  Jevons.  identifies  induction  with  scientific 
method  in  general;  it  consists  of  forming  hypotheses,  deducing 
their  consequences,  and  verifying  them.  The  first  step  in  the 
process,  the  passage  from  the  particular  to  the  universal,  Sig- 

^Logic,  vol.  II,  chap,  v,  §93,  14. 
^'Logic,  vol.  II,  chap,  v,  §93,  15. 
^LogiC)  vol.  II,  chap,  v,  §93,  17.  Note  2. 


20  UNIVERSITY  OF  MISSOURI  STUDIES  [l68 

wart  bases  on  the  principle  that  the  given  is  necessary :  there  is 
:i  necessary  connection  between  things,  they  are  related  as 
ground  and  consequent  so  that  when  one  appears  the  other  must 
appear  also.  "Every  particular  perception  is  an  instance  of  a 
general  rule.''  This  principle  is  not.  however,  as  with  Mill  and 
Jevons,  derived  from  experience,  but  is  a  postulate  of  our  think- 
ing.3® 

3»Somewhat  similar  to  Sigwart's  conception  is  that  of  Ueberweg. 
According  to  him,  the  incomplete  induction  would,  according  to  the 
rules  of  the  syllogism,  justify  only  a  particular  conclusion.  The  valid- 
ity of  the  generalization  of  the  conclusion  rests  partly  upon  the  general 
assumption  of  a  lawful  causal  nexus  in  the  objects  of  our  knowledge, 
partly  upon  the  special  assumption  that  in  the  given  case  some  lawful 
causal  nexus  exists  between  the  subject  and  predicate  of  the  conclusion. 
The  import  of  induction  as  a  means  of  extending  our  knowledge  rests 
upon  the  same  relation  to  the  real  uniformity  (according  to  the  princi- 
ple of  ground)  on  which  the  possibility  of  the  syllogism  as  a  form  of 
knowledge  is  founded.  The  existence  of  the  causal  nexus  precedes  our 
inductions.  Our  knowledge  of  the  causal  nexus  in  a  particular  case 
presupposes  a  collection  of  facts,  and  our  knowledge  of  the  causal  nexus 
in  general  form  follows  upon  many  special  inductions.  This  knowledge 
is  the  condition  (not  of  these  inductions,  in  which  case  we  should  have 
a  circulus  vitiosus,  but  only)  of  the  logical  justification  of  these  induc- 
tions. We  at  first  generalize  only  according  to  psychical  laws  of  asso- 
ciation ;  our  generalizations  have  logical  justification  in  so  far  as  they 
invariably  coincide  with  the  objective  causal  nexus.      System  der  Lo^ik, 

§§I27ff. 

The  same  idea  is  very  clearly  brought  out  by  Creighton  in  his  Intro- 
ductory Logic,  §88.  In  induction,  he  tells  us,  we  begin  with  particular  phe- 
nomena, and  try  to  discover  from  them  the  law  or  principle  which 
unites  them.  Certain  facts  are  observed  to  happen  together,  and  the 
problem  is  to  find  the  ground  or  explanation  of  this  connection.  In- 
ductive inference  is  thus  a  process  of  reading  the  general  law  out  of  the 
particular  facts.  It  is  an  insight  into  the  nature  of  the  whole  or  system, 
based  upon  the  careful  examination  of  the  parts.  Inference  alwavs  im- 
plies an  effort  on  part  of  the  mind   to   see   how  phenomena  are  neces- 


169]  THE  PROCESS  OF  INDUCTIVE  INFERENCE  21 

§  6.  Lotze  ^^  declares  that  "in  attaining  to  universal 
propositions  of  the  form  all  S  are  M,  induction  has  reached  its 
first  goal,  and  it  is  possible  to  rest  content  with  the  result,  espec- 
ially when  we  are  dealing  with  a  question  of  practical  life;  for 
in  such  questions  we  can  go  without  a  reason,  so  long  as  we  are 
certain  that  as  a  matter  of  fact  M  is  really  true  of  all  instances 
of  S,  say  of  all  men;  we  do  not  care  so  much  to  know  whv  it 
•holds  of  them,  and  why  only  of  them  and  not  perhaps  of  animals 
as  well.  The  theoretic  impulse  however  is  not  satisfied  with 
merely  joining  M  to  its  proximate  subject;  it  would  fain  seek 
out  within  the  limits  of  S  the  narrower  group  of  attributes,  which 
contains  the  ground  of  this  coniunction.  and  which  conditions 
the  same  attribute,  wherever  it  may  occur,  perhaps  even  outside 

&arilj  connected  according  to  some  general  principle.  And  in  carrying 
out  this  purpose,  the  mind  must  begin  with  the  knowledge  which  it  al- 
ready possesses.  When  the  general  law  of  connection  is  known,  and 
the  object  is  to  discover  the  nature  of  some  particular  fact,  the  method 
ot  procedure  is  deductive.  But  when  the  problem  by  which  we  are  con- 
fronted is  to  read  out  of  the  facts  of  sense  perception  the  general  law  of 
their  connection,  the  method  of  inference  which  must  be  employed  is 
that  of  induction.  But  from  whatever  point  we  set  out,  and  whatever 
may  be  the  immediate  object  of  the  inference,  the  result  is  always  the 
same — an  insight  into  the  necessary  connection  of  tacts  according  to 
some  general  principle.  The  essential  point  is  to  detect  the  general 
law  or  principle,  and  for  this  purpose  one  case  may  conceivably  be  as 
good  as  a  hundred.  Inductive  inference,  then,  is  not  a  process  of  pass- 
ing from  a  certain  number  of  cases  to  a  general  conclusion  which  always 
remains  probable  because  it  has  no  proper  justification.  But  its  real 
nature  consists  in  the  discover}',  through  the  aid  of  examples,  of  a  uni- 
versal law  ot  connection.  See  also,  the  able  works  oi  Hihhen. /nduciive 
Logic,  and  Welton,  A  Manual  of  Logic,  volume  II. 

""Los^ic,  English  translation,  edited  by  Bernard  Bosanquet;  Outlines 
of  Losric,  translated  by  G.  T.  Ladd.  These  translations  have  been  used 
bv  me  in  the  text. 


2  2  UNIVERSITY  OF  MISSOURI  STUDIES  [  I  70 

S.     Then  the  induction  is  pushed  further;  we  use  a  series  of 
.universal  propositions  of  the  form:  SM,  RM,  TM,  ...  as  our 
now  premises  and  try  to  deduce  from  them  an  universal  conclu- 
sion of  the  form  all  2  are  M.     In  this  new  conclusion  we  under- 
stand and  denote  by  2  the  true  subject  or  the  conception  of  the 
genus,  or,  to  put  it  in  another  way,  that  complex  of  attributes, 
on  which  the  predicate  M  in  all  cases  depends  and  from  which  it 
results.  Thus  in  our  first  induction  we  shall  reach  the  proposition 
SM  ;  in  all  animals  an  exchange  of  gas  takes  place  in  respiration ; 
in  a  second  induction  in  which  S  is  successively  replaced  by  birds, 
fishes,   and  amphibia,   we  shall   reach  the  conclusion  2M,   all 
animals  require  an  exchange  of  gases.     This  new  conclusion  at 
once  throws  light  on  the  earlier  one,  by  showing  that  what  we 
had  hitherto  only  observed  as  an  isolated  fact  is  really  necessi- 
tated by  the  universal  nature  of  animal  life;  a  third  induction 
sets  alongside  of  2M  a  new  premise  to  the  same  effect,  viz. 
all  plants  display  though  in  another  way  the  phenomenon  of  a 
change  of  gas;  its  conclusion  SM,  all  organic  beings  whatever 
find  themselves  in  like  case,  shows  us  the  phenomenon  in  question 
bound  up  with  a  still  more  universal  subject,  and  lastly  by  com- 
paring the  behavior  of  bodies  which   resemble  organic  bodies 
in  structure  towards  the  surrounding  atmosphere  we  might  be 
led  to  the  thought  that  under  the  conditions  prevalent  on  the 
earth's  surface,  such  an  exchange  of  material  is  absolutely  neces- 
sary to  the  development  of  those  interdependent  processes  of 
change,  which  make  up  organic  life.     In  all  this  it  is  to  be  no- 
ticed that  the  further  we  advance  these  inductions  the  less  do 
we  care  to  obtain  as  our  result  a  categorical  judgment  of  the 
form  S  is  P;  we  are  no  longer  seeking  the  highest  general 
conception,  to  which  a  given  phenomenon  attaches  a  predi- 
cate; what  we  are  in  search  of  is   a  hypothetical  judgment, 


171]  THE  PROCESS  OF  INDUCTIVE  INFERENCE  23 

which  will  acquaint  us  with  the  most  general  condition  C, 
upon  which  the  phenomenon  always  depends  and  of  which 
it  is  the  consequence  wherever  it  occurs."  *^ 

"Stated  in  its  complete  logical  form  a  law  is  alwa3^s  a  uni- 
versal hypothetical  judgment  which  states  that  whenever  C  is 
or  holds  good,  2  is  or  holds  good,  and  that  whenever  C  under- 
goes a  definite  change  into  Q}  through  a  variation  of  itself, 
dC,  E  also  becomes  E^  through  a  definite  variation  of  itself  dE 
which  depends  on  dC.  A  law  is  hypothetical,  because  it  is 
never  meant  to  be  a  mere  enumeration  of  what  happens ;  its  sole 
function  is  to  determine  what  should  or  must  happen  when  cer- 
tain conditions  are  given."  ^^  "In  theoretical  investigations  of 
reality,  we  mean  by  a  law  the  expression  of  the  peculiar  inward 
relation  which  exists  between  two  facts  and  constitutes  the 
ground  at  once  of  their  coniunction;  and  in  every  single  case 
there  is  but  one  law."  ■^^ 

The  logical  idea  upon  which  induction  rests  is  by  no  means 
merely  probable,  but  certain  and  irrefragable.  It  consists  in  the 
conviction,  based  upon  the  principle  of  identity,  that  every  de- 
terminate phenomenon  M  can  depend  only  upon  one  determinate 
condition,  and  accordingly  that,  where  under  apparently  different 
circumstances  or  in  different  subiects  P,  S,  T,  U  the  same  M 
occurs,  there  must  inevitably  be  in  them  some  common  element 

^^Logic,  vol.  II,  pp.  35  £f.  See  also,  OatUties  of  Logic,  pp.  72  ff,, 
121  ff .  Outlines,  p.  123:  "That  is  to  say,  it  is  only  rarely  of  much  use 
to  us  to  show  that  a  P  is  united  with  a  general  generic  concept  S,  and 
belongs  to  all  species  of  S.  As  a  rule,  we  desire  still  further  to  know 
on  vihdit ground  P  belongs  to  S.  This,  expressed  in  general  form,  leads 
to  the  problem  of  searching  for  the  conditions  on  which  the  occurrence 
of  an  event  depends  in  all  the  otherwise  diverse  instances  of  its  repeti- 
tion." 

^Logic,  vol.  II,  p.  68. 

^'^Logic,  vol.  II,   p.  71. 


H 


UNIVERSITY  OF  MISSOURI  STUDIES  [172 


:i.  which  is  the  true  identical  condition  of  M  or  the  true  subject 

of  -M.-"-* 

"It  would  be  quite  unjustifiable  to  object,  that  as  a  matter  of 
experience  the  same  consequence  M  is  often  produced  by  differ- 
ent equivalent  conditions,  and  the  same  predicate  M  may  occur 
in  extremely  different  subjects.  If  there  are  two  equivalent  con- 
ditions for  a  result  M,  it  is  not  -  in  virtue  of  that  which  makes 
them  different,  P  or  S,  but  of  that  which  is  the  ground  of  their 
equivalence,  that  they  are  really  conditions  of  the  same  result: 
so  long  as  we  cannot  separate  this  common  characteristic  in  the 
two,  we  have  not  yet  found  the  true  2  of  the  conclusion,  and 
have  not  therefore  carried  out  the  induction  in  the  way  in  which 
it  demands  to  be  carried  out.  Again,  if  the  same  M  is  found  as 
predicate  in  a  number  of  extremely  different  subjects,  and  sub- 
jects (as  is  usually  the  case  in  practice)  the  several  sums  of 

«Zo^ic,  vol.  II,  English  translation,  p.  23:  "The  law  of  identity 
guarantees  that  if  the  same  S  were  once  more  perceived  in  a  second  ex- 
perience it  would  be  impossible  that  the  same  predicate  P  should  be 
absent  or  should  be  replaced  by  some  other  predicate  Q."  Outlines  of 
Log-ic,  p.  120:  "It  follows  from  the  law  of  identity,  that  a  truth  which 
is  valid  once  can  not  fail  to  be  valid  a  second  time;  accordingly  that 
tvery  individual  experience  is  once  for  all  valid — that  is  to  say,  the  same 
predicate  is  again  valid  at  all  times  for  all  cases  of  the  recurrence  of  the 
same  subject.  The  difficult  thing  is  simply  to  determine  in  praxi 
whether  a  second  instance  does  actually  repeat  precisely  the  subject  ob- 
served in  the  first  case.  For  this  the  probabilities  are  different  in  differ- 
ent domains  of  research.  For  example,  it  is  enough  for  the  chemist,  if 
he  once  knows  that  he  has  some  element  before  him  in  a  pure  state,  to 
observe  its  reaction  towards  some  other  element  a  single  time,  in  order 
to  establish  it  forever.  The  zoologist,  on  the  contrary,  will  hold  some 
peculiarity  of  a  new  animal,  only  one  example  of  which  has  been  dis- 
covered, to  be  'normal,'  that  is,  to  be  valid  in  general  (since  disease  and 
malformation  are  possible  in  such  a  case),  only  when  the  analogies  of 
other  classes  of  animals  justify  him  in  this  assumption." 


173]  THE  PROCESS  OF  INDUCTIVE  INFERENCE  25 

whose  marks  are  only  partially  known,  we  may  of  course  make  a 
great  mistake  if  we  combine  what  is  common  to  the  known 
marks  of  all  of  Ihem,  and  then  assume  it  to  be  2,  the  true  subject 
of  the  mark  in  question  M.  I  do  not  deny  that  in  the  practice 
of  induction  we  are  often  placed  in  such  unfavorable  circum- 
stances; but  all  these  difficulties  in  carrying  out  the  inductive 
principle  do  not  alter  its  universal  logical  validity,  when  it  asserts 
that  wherever  different  conditions  have  the  same  result  M,  or 
different  subjects  the  same  predicate  M,  there  must  be  discover- 
able one  and  only  one  determinate  2,  forming  the  single  invari- 
able condition  or  the  single  true  subject,  to  which  the  predicate 
or  the  result  M  is  to  be  universally  and  necessarily  ascribed  in  a 
conclusion  of  the  form,  'every  2  is  M.'  "  ^^ 

That  is,  induction  is  founded  on  the  principle  that  every 
phenomenon  has  its  definite  condition,  and  this  condition  is  al- 
ways the  same.  There  is  uniformity  in  nature,  whatever  has 
happened  will  happen  again  and  will  happen  as  it  happened  be- 
fore.^^     Things  are  identical  with  themselves:  whatever  is  re- 

^Logic,  vol.  I,  pp.  i36f. 

^Logic,  vol.  II,  p.  25:  "Once  suppose  that  a  single  observed  case  is 
valid  only  for  itself  and  not  for  its  repetitions  in  like  case  •  »  • 
once  suppose  that  with  like  obiect  and  like  conditions  a  different  result 
may  be  true,  and  there  is  an  end  to  all  possibility  of  developing  univer- 
sal truths  from  experience;  there  is  an  end  not  merelv  to  the  discoverv 
ot  laws  but  to  the  use  of  the  word  'law'  with  any  intelligible  meaning. 
The  art  of  induction,  which  is  to  bring  us  to  universal  laws,  rests  whollv 
on  the  acumen  shown  in  developing  pure  and  self-connected  propositions 
of  the  form  Z  is  U  out  of  the  impure  and  confused  material  of  our  per- 
ceptions, which  come  to  us  in  the  form  S  is  P  " 


,5  UNIVERSITY  OF  MISSOURI  STUDIES  [174 

mains  what  it  is.-*'      Induction  is  therefore  ultimately  based  by 
Lotze  on  the  principle  of  identity.*'^. 

-•"Compare  this  idea  with  the  statement  in  Outlines,  pp.  l\i:  "This 
simple  logical  meaning  ot  the  proposition  [of  identity  A=A]  must 
without  fail  be  distinguished  from  other  theorems,  partly  true,  partly 
doubtful,  which,  although  they  spring  from  the  application  of  the  uni- 
versal logical  proposition  of  identity,  still  do  so  only  from  its  applica- 
tion to  a  definite  real  content,  and  are  not  on  a  par  with  the  proposition 
itself.  For  example,  that  every  'thing'  is  like  itself,  or  that  it  is  un- 
changeably like  itself,  is  a  metaphysical  proposition  which  arises  from 
an  application  of  the  logical  proposition  of  identity  to  the  concept  of  the 
'existent.'  The  logical  proposition  itself  says  nothing  at  all  of  'things.' 
It  is  also  valid  of  events  that  happen,  of  conditions  that  take  place,  of 
the  real  as  truly  as  of  the  unreal.  And  of  all  of  them  it  merely  says, 
that  to  be  is  to  be,  the  changeable  is  changeable,  the  contradictory  is 
contradictory,  the  impossible  is  impossible."  I  do  not  see  how  this 
thought  agrees  with  the  notion  that  the  idea  on  which  induction  is 
based  is  certain  and  irrefragable. 

■•"According  to  Kromann,  Unsre  Naturerkenntniss,  all  logic  is  based 
upon  the  law  of  identity.  Hence  induction,  to  be  a  logical  process  at 
all,  must  obey  this  law,  or  must  be  perfect,  i.  e.,  as  much  must  be  con- 
tained in  the  premises  as  is  contained  in  the  conclusion.  It  would  have 
the  following  form:  This  oxygen  has  a  specific  gravity  of  16:  all 
oxygen  is  like  this  with  respect  to  its  specific  gravity;  hence  all  oxygen 
has  a  specific  gravity  of  16.  Or  it  may  read  as  follows:  This  oxygen 
has  a  specific  gravity  of  16;  all  oxygen  is  probably  like  this  with  respect, 
etc.;  hence  all  oxygen  has  probably  a  specific  gravity  of  16.  The  in- 
duction is  based  on  the  identity  of  the  examined  case  with  all  other 
cases  of  the  same  kind.  The  principle  of  identity:  the  world  is  ident- 
ical with  itself,  every  thing  is  what  it  is,  is  not  the  result  of  experience, 
but  a  postulate,  a  primary  hypothesis  with  which  we  approach  the  in- 
vestigation of  reality.  It  is  a  necessary  postulate  of  the  will  to  live:  the 
acceptance  of  it  makes  life  possible.  See  also  Bosanquet,  Logic,  Essen- 
tials of  Logic,  pp.  153,  162,  165. 


PART   II 

The  Theory  of  Induction  ^ 

§  I.  An  examination  of  the  different  theories  of  induction 
shows  us  that  there  are  two  questions  at  issue:  (i) 
What  is  the  nature  of  the  process  called  induction?  And  (2), 
What  is  the  validity  of  the  process  ? 

The  first  question  is  answered  as  follows :  Induction  is  defined 
in  a  general  way  as  a  process  of  inferring  from  the  particular  to 
the  universal.  That  is,  whenever  we  derive  a  general  statement 
from  a  particular  statement  or  facts,  we  have  induction.  Most 
writers  would  be  willing  to  accept  this  as  a  rough  definition  of 
the  process.  Some  distinguish  between  scientific  induction  and 
unscientific  induction,  but  look  upon  both  forms  as  coming  under 
the  definition.2  Others,  however,  reject  the  unscientific  form,  or 
simple  enumeration,  and  accept  only  that  phase  of  induction 
which  derives  from  particular  facts  the  law  of  their  necessary 
connection.  According  to  them,  induction  seeks  to  discover  not 
the  casual,  but  the  causal  connections.^     Of  these,  some  identify 

iRead  before  the  pint  meeting  of  the  American  Psychological 
Association  and  the  Western  Philosophical  Association,  Chicago,  Janu- 
ary I,  1902,  and  published  in  the  Philosophical  Review  of  July,  1903. 

2Bacon,  Mill,  Veitch,  Lotze,  Wundt. 

^Sigwart,  Ueberweg,  Bosanquet,  Hibben,  Welton,  Creighton;  Shute, 
Discourse  on  Truth;  Hamelin,  Sur  V induction. 
175]  27 


28 


UNIVERSITY  OF  MISSOURI  STUDIES  [176 


induction  with  scientific  method  in  general,  including  under  it  the 
forming  of  hypotheses,  deducing  their  consequences,  and  verify- 
ing tliem."* 

The  second  question  also  receives  various  answers.  Ac- 
cording to  some  thinkers,  only  so-called  perfect  induction  is  cer- 
tain :  imperfect  induction  is  merely  probable.^  Nearly  all  seem 
to  agree,  however,  that  induction  is  grounded  on  the  principle 
of  the  uniformity  of  nature.  This  principle  is  interpreted  differ- 
ently bv  different  thinkers,  sometimes  merely  called  by  another 
name.  Some  speak  of  it  as  the  principle  of  identity.  What 
is  once  true  will  always  be  true ;  whatever  is,  will  remain  so :  the 
world  is  identical  with  itself.^  Some  express  the  same  idea  by 
saving  that  the  particular  is  the  expression  of  the  universal.'^ 
Some  call  the  principle  the  principle  of  necessary  connection :  the 
given  is  necessary .^  Some  identify  it  with  the  law  of  causation : 
every  event  must  have  some  cause.^ 

Moreover,  this  principle  of  uniformity  is  conceived  by  some 

■•Sigwart,  Jevons,  Hamelin. 

^Apelt,  Whately,  Jevons. 

^Lotze,  Kromann,  Bosanquet. 

'Aristotle,  Hegel. 

^Sigwart,  Ueberweg,  Hibben,  Welton,  Creighton. — Venn,  Empirical 
and /uducfive  Lo£-ic,  defines  it  thus:  "Perhaps  indeed  as  near  an  ap- 
proach as  we  can  get  to  any  definition  is  reached  by  saying  that  wherever 
any  two  or  more  attributes  are  repeatedly  found  to  be  connected  to- 
gether, closely  or  remotely,  in  time  or  in  space,  there  we  have  a  uni- 
formity. And  the  general  expression,  the  uniformity  of  nature,  is  in- 
tended to  cover  all  such  partial  connections,  and  to  imply  that  their  ex- 
istence may  be  detected  or  reasonably  inferred  throughout  all  phenom- 
ena whatever"  (p.  93). 

''Mill,  Jevons,  Veitch,  Benno  Erdmann. 


177]  THE  PROCESS  OF  INDUCTIVE  INFERENCE  2g 

as  a  postulate  of  our  thinking,^^  by  others  as  the  product  of  ex- 
perience.^^ 

§  2.  Let  us  now  attempt  to  answer  the  first  question: 
What  is  the  nature  of  induction  ?  Induction  is  a  process  of  in- 
ference. We  must  be  careful  to  distinguish  between  inference 
and  association  of  ideas.  The  perception  of  fire  may  arouse  in 
the  child's  conscimisness  the  thought  of  a  burn,  simply  because 
these  two  things  have  been  experienced  together  before.  A 
knock  at  the  door  may  arouse  in  my  consciousness  the  image  of 
a  man  making  certain  movements.  But  in  neither  case  is  there 
necessarily  inference.  In  order  to  infer,  I  must  consciously 
relate  one  judgment  with  another.  I  must  ground  it  on  some 
other  judgment,  or  draw  it  from  some  other  judgment.  I  must 
say,  Because  this  is  so,  that  is  so;  or,  this  is  so,  therefore 
that  is  so.  In  the  words  of  Ladd:  "The  thinking  subject 
reaches  genuine  logical  inference  whenever  two  judgments  are 
related  in  such  manner  that  one  is  made  the  'reason'  or  'ground' 
of  the  other,  with  a  consciousness  of  the  relation  thus  estab- 
lished between  them."  ^^  There  are  two  kinds  of  reasoning,  de- 
duction and  induction.  Both  are  processes  of  inference,  and 
therefore  essentially  the  same,  that  is,  both  consciously  relate 
judgments  with  other  judgments.  In  both  cases  a  certain  judg- 
ment is  accepted  on  the  ground  of  another;  this  is  so,  we  say, 
because  that  is  so;  or,  this  is  so,  therefore  that  is  so.     The  dif- 

i^Sigwart,  Lotze,  Kromann,  Bosanquet,  Hibben,  Welton,  Creigh- 
ton. — Venn,  Empirical  Logic :  "I  am  very  decidedly  of  opinion  that  the 
difficulty  does  not  admit  of  any  logical  solution.  It  must  be  assumed  as 
a  postulate,  so  far  as  logic  is  concerned,  that  the  belief  in  the  Uniform- 
ity of  Nature  exists,  and  the  problem  of  accounting  for  it  must  be  rele- 
gated to  Psychology"  (pp.  131  f). 

"Mill,  Jevons,  Benno  Erdmann. 

^Psychology,  Descriptive  aiid  Explanatory,  pp.  463  f. 


go  UNIVERSITY  OF  MISSOURI  STUDIES  [178 

ference  between  the  processes  consists  in  this ;  in  induction  we 
ground  our  judgment  on  particular  instances,  that  is,  pass  from 
particulars  to  a  universal  proposition  concerning  them;  while 
in  deduction  we  ground  our  judgment  on  a  universal  proposi- 
tion, that  is,  we  start  from  a  universal  proposition  and  draw  from 
it  other  propositions  according  to  the  principle  of  identity.  "In 
induction,  then,  we  conclude  that  all  A  is  B,  because  we  have 
observed  that  ai  and  a2  (all  essentially  alike  and  capable  of  be- 
ing grouped  under  A)  are  B.  In  deduction  we  know,  or  assume 
as  known,  that  A  is  B,  and  conclude  that  a3  (which  we  have 
never  met  with  before)  is  B."  ^^  When  I  infer  that  all  swans 
are  white,  because  the  swans  I  have  seen  were  white,  I  am  reas- 
oning inductively.  In  induction  we  leap  from  a  particular  case 
or  cases  to  all ;  we  infer  that  because  a  certain  thing  is  true  of  a 
certain  case  or  cases,  it  is  true  for  all  cases  resembling  the  others. 

And  here  it  is  well  to  remember  several  important  points. 
I.  So  far  as  the  principle  is  concerned,  it  makes  no  difference 
whether  the  induction  is  true  or  false.  It  is  just  as  much  an  in- 
ductive inference  to  conclude  that  all  crows  are  black  because 
some  are,  as  to  conclude  that  all  men  are  mortal  because  some 
are.  Hasty  induction  is  induction,  as  much  so  as  careful  and 
scientific  induction.  The  characteristic  mark  of  induction  con- 
sists in  making  the  so-called  "inductive  leap,"  in  jumping  from 
one  or  more  instances  to  a  general  conclusion.^* 

2.  Nor  is  it  correct  to  limit  induction  to  the  discovery  of 
causal  relations.  Whenever  we  infer  a  universal  statement  from 
a  particular  case  or  cases,  leap  from  the  particular  to  the  uni- 
versal, we  have  induction.     We  do  not  strive  to  know  merely  the 

^^Ladd,  Psychology,  p.  478. 

^^"An  imperfect,  hasty,  or  unwarranted  induction  is  still  an  induc- 
tion, only  a  bad  one."  Veitch,  Z.£>^/c,  p.  461.  See  also  Mill,  Logic 
Bk.  Ill,  chap,  iv,  §3  note. 


179]  THE  PROCESS  OF  INDUCTIVE  INFERENCE  3 1 

causes  of  things ;  we  are  interested  in  other  relations  also,  for  in- 
stance, in  the  co-existence  of  certain  qualities,  whether  they  are 
causally  related  or  not.^^  Our  purpose  is  to  discover  regularity, 
uniformity  everywhere.  Of  course,  if  we  identify  causality  with 
uniformity,  as  some  writers  do,  if  we  call  all  those  relations 
causal  in  which  there  is  uniformity  of  sequence  or  co-existence, 
then  induction  means  to  discover  causality.  But  if  we  do  not 
define  causality  that  way,  if  we  do  not  conceive  all  uniform  se- 
quences and  co-existences  as  causally  related,  then  we  cannot 
define  induction  as  the  quest  for  causal  relations ;  for,  as  was  al- 
ready said,  we  are  interested  in  all  kinds  of  regularity  or  orderli- 
ness. It  is  true  that,  wherever  we  find  such  regularity,  we  are 
tempted  to  read  causality  into  it ;  but  that  is  another  story, 

3.  And  this  leads  us  to  another  point.  It  is  held  by  many 
writers  that  induction  seeks  to  discover  the  inner,  necessary  rela- 
tions existing  between  things.  In  a  certain  sense,  this  is  true. 
The  thinker  is  always  eager  to  find  out  what  qualities  are  con- 
nected necessarily,  that  is,  he  wants  to  feel  not  only  that  certain 
qualities  go  together,  but  that  they  must  somehow  go  together. 
He  is  not  satisfied  with  the  statement  that  all  swans  are  white, 
because  he  does  not  understand  the  inner  relation  existing  be- 
tween swan  nature  and  whiteness,  he  does  not  see  why  swans 
should  be  white,  he  does  not  see  any  necessary  relation  here. 
He  seeks  to  discover  connections  between  things  which  will  sat- 
isfy him.  "Take,  for  instance,  the  simple  effect  of  hot  water 
cracking  glass.  This  is  usually  learnt  empirically.  Most  people 
have  a  confused  idea  that  hot  water  has  a  natural  and  inevitable 
tendency  to  break  glass,  and  that  thin  glass,  being  more  fragile 
than  other  glass,  will  be  more  easily  broken  by  hot  water. 
Physical  science,  however,  gives  a  very  clear  reason  for  the  effect 

isSee  Veitch,  Logic,  p.  461;  Venn,  Logic,  p.  93;   Sigwart,  Logik. 


o 


2  UNIVERSITY  OF  MISSOURI  STUDIES  [l8o 


In  sliowing  that  it  is  only  one  case  of  the  general  tendency  of 
heat  to  expand  substances.  The  crack  is  caused  by  the  success- 
ful effort  of  the  heated  glass  to  expand  in  spite  of  the  colder  glass 
witli  which  it  is  connected."  ^^  That  is,  the  scientist  aims  to 
bring  his  proposition  under  a  proposition  which  is  more  general 
in  its  scope,  one  which  expresses  a  more  constant  connection  be- 
tween objects  than  the  other,  and  therefore  impresses  us  as  nec- 
essary. He  seeks  for  a  simple  formula  under  which  he  can  em- 
brace a  great  many  cases  that  seem  to  have  nothing  at  all  in  com- 
mon. "Suppose  some  one  observes  that  (a)  the  addition  of  fuel, 
(b)  the  action  of  blowing,  and  (c)  cold  weather  increase  the 
flame  of  the  fire.  He  may  at  first  be  satisfied  with  the  assump- 
tion that  every  one  of  these  three  phenomena  is  a  cause  of  the  in- 
crease of  the  flame.  But  when  he  discovers  a  great  number  of 
phenomena  which  are  followed  by  an  increase  of  flame,  he  finds 
it  hard  to  think  of  them  all.  But  if  he  can  find  that  every  time 
the  flame  is  increased,  something  was  added  to  the  fire  which, 
according  to  analysis,  contains  oxygen,  he  will  reduce  the  mani- 
fold experiences  to  the  simple  formula :  All  things  which  contain 
oxygen  and  are  added  to  fire  increase  the  flame.  He  will  prob- 
ably go  farther  and  say:  Oxygen  is  the  cause  of  the  increase 
of  the  flame."  ^7 

The  truth  is,  the  thinker  aims  to  understand  his  facts,  that 
is,  to  assimilate  them  to  the  known,  to  bring  them  into  relation 
with  what  he  already  knows.  You  tell  him  that  heat  cracks  the 
glass  because  heat  is  motion,  expansive  motion ;  he  understands 
that  because  he  has  seen  many  examples  of  motion  breaking 
things.  "We  did  not  reject  the  assertion  that  there  are  black 
swans,"  says  Mill,  "while  we  should  refuse  credence  to  any 

^®Je\ons,  Lessons  in  Logic,  p.  257. 

i^Uphues,  Grtmdlegung    der    Logik;  Nach    Shute's    Discourse    on 
Truth  bearbeitet,  p.  182. 


l8l]  THE  PROCESS  OF  INDUCTIVE  INFERENCE  33 

testimony  which  asserted  that  there  were  men  wearing  their 
heads  underneath  their  shoulders.  The  first  assertion  was  more 
credible  than  the  latter.  But  why  more  credible?  So  long  as 
neither  phenomenon  had  actually  been  witnessed,  what  reason 
was  there  for  finding  the  one  harder  to  be  believed  than  the  other  ? 
Apparently  because  there  is  less  constancy  in  the  colors  of  ani- 
mals than  in  the  general  structure  of  their  anatomy.  But  how- 
do  we  know  this?  Doubtless,  from  experience.  Experience 
testifies  that  among  the  uniformities  which  it  exhibits  or  seems 
to  exhibit,  some  are  more  to  be  relied  upon  than  others."  ^^  But 
it  must  not  be  forgotten  here  that  it  is  induction  to  conclude  from 
our  observations  that  heat  cracks  glass,  that  blowing  makes  the 
fire  burn,  that  chlorine  bleaches,  even  if  we  do  not  understand 
the  reasons  or  see  the  so-called  necessary  connections.  "We 
learn  empirically  that  a  certain  strong  yellow  color  at  sunset,  or 
an  unusual  clearness  in  the  air,  portends  rain ;  that  a  quick  pulse 
indicates  fever;  that  horned  animals  are  always  ruminants;  that 
quinine  affects  beneficially  the  nervous  system  and  the  health  of 
the  body  generally;  that  strychnine  has  a  terrible  effect  of  the 
opposite  nature;  all  these  are  known  to  be  true  by  repeated  ob- 
servation, but  we  can  give  no  other  reason  for  their  being  true, 
that  is,  we  cannot  bring  them  into  harmony  with  any  other  scien- 
tific facts ;  nor  could  we  at  all  have  deduced  them  or  anticipated 
them  on  the  ground  of  previous  knowledge."  ^^  Induction  is 
induction,  whether  we  can  bring  it  into  harmony  with  other  scien- 
tific facts  or  not.  It  must  further  be  remembered  that  deduction 
frequently  enters  into  those  cases  in  which  we  reach  so-called 
necessary  connections.  I  discover  by  induction  that  heat  cracks 
glass.  I  refer  this  empirical  law  to  a  larger  induction,  that  heat 
expands  substances.     I  say  heat  must  crack  glass  under  certain 

^^Lo£'ic,  Bk.  Ill,  ch.  iv.     See  also  ch.  iii. 
^^Jevons,  LessoMs,  p.  256. 
(3) 


24  UNIVEKSITV  OF   MISSOURI  STUDIES  [iSz 

circunistances,  because  heat  expands  substances.  If  heat  expands 
substances,  it  must  expand  glass ;  and  if  the  colder  parts  of  the 
o-lass  connected  with  the  heated  parts  do  not  expand  fast  enough, 
the  glass  will  break.  This  is  really  deduction.  I  subsume  the 
case  under  a  general  rule.  I  think  I  understand  it  better  when 
I  see  that  it  is  really  an  instance  of  a  general  occurrence  with 
which  I  am  very  familiar. 

4.  This  brings  us  to  another  point.  Several  thinkers  de- 
fine induction  as  forming  hypotheses,  drawing  their  conse- 
quences, and  verifying  them.  This,  it  seems  to  me,  is  a  false 
definition.  If  we  define  it  in  this  way,  then  we  apply  the  name 
induction  to  different  operations,  we  include  under  it  both  in- 
duction and  deduction.  If  induction  is  both  induction  and  de- 
duction, then  what  is  the  process  called  induction,  which  with 
deduction  constitutes  induction?  Of  course,  we  may,  if  we 
choose,  apply  the  term  induction  to  scientific  methods  in  gen- 
eral, to  the  method  which  everybody  uses  in  the  pursuit  of  truth, 
and  which  embraces  all  the  operations  of  the  mind  that  lead  to 
truth.  But  in  that  case  what  is  the  process  called  induction 
proper?  And  why  should  we  use  one  term  for  two  processes, 
first  for  a  combination  of  induction  and  deduction,  then  for  in- 
duction itself?  The  logical  thing  to  do  is  to  restrict  the  term  in- 
duction to  induction  proper,  to  the  process  of  inferring  a  general 
truth  from  particular  instances,  and  to  use  another  name  for  the 
combination  of  this  process  with  deduction.  In  his  smaller  book 
Jevons  calls  this  method,  which  he  designates  as  induction  in  his 
Principles  of  Science,  the  combined  or  complete  method.  "What 
Mr.  Mill  has  called  the  deductive  method,  but  which  I  think 
might  more  appropriately  be  called  the  combined  or  complete 
method,  consists  in  the  alternate  use  of  induction  and  deduction. 
It  may  be  said  to  have  three  steps,  as  follows: — (i)  Direct  in- 
duction ;  (2)  Deduction,  or,  as  Mr.  Mill  calls  it,  ratiocination;  (3) 


183]  THE  PROCESS  OF  INDUCTIVE    INFERENCE 


35 


Verification.  The  first  process  consists  in  such  a  rough  and  simple 
appeal  to  experience  as  may  give  us  a  glimpse  of  the  laws  which 
operate,  without  being  sufficient  to  establish  their  truth.  Assum- 
ing them  as  provisionally  true,  we  then  proceed  to  argue  to 
their  effects  in  other  cases,  and  a  further  appeal  to  experience 
either  verifies  or  negatives  the  truth  of  the  laws  assumed."  20 

5.  There  is  another  point  to  be  observed.  It  is  held  that 
when  I  infer  from  one  or  more  cases  to  all  like  them,  I  base 
myself  either  consciously  or  unconsciously  on  the  principle  of 
the  uniformity  of  nature.  That  is,  I  reason  thus :  This  is  true 
of  these  cases;  what  is  true  of  some  cases  is  true  of  all  like 
them;  hence  this  is  true  of  all.  In  other  words,  induction  is 
really  deduction.  This,  however,  does  not  seem  to  me  to  be 
the  case.  In  fact,  the  statement  that  what  is  true  in  some  cases 
is  true  in  every  case  like  them,  is  the  very  thing  that  is  inferred 
in  induction.  We  infer  that  this  will  always  happen  because  it 
has  happened.  As  soon  as  we  observe  the  co-existence  or 
sequence  of  certain  qualities  several  times,  we  naturally  draw 
our  conclusion,  we  make  the  inductive  leap.  We  say,  sometimes, 
hence,  always.  Why  we  do  so,  it  is  impossible  to  say;  it  is  one 
of  those  inexplicable  facts,  a  natural  function  of  the  human  mind, 
a  way  we  have  of  thinking,  that  is  all.  We  expect  repetition. 
We  may  have  no  right  to  expect  it,  but  the  fact  remains  that  we 
do  expect  it  and  conclude  that  it  will  come.  We  infer  when  we 
find  a  ground  or  reason  for  our  proposition.  Everything  is  a 
ground  for  us  that  really  satisfies  us.  Closer  thinking  may 
destroy  our  satisfaction,  but  so  long  as  we  have  grounded  our 
proposition  upon  some  other  proposition  and  are  satisfied,  we 
have  reasoned.  We  may  have  reasoned  wrong,  but  we  have 
reasoned.  Inductive  inference  is  a  function  of  the  mind  aroused 
by  the  experience  of  recurrence,  in  which  we  regard  the  par- 

^Lessons  in  Logic,  pp.  258  f.     Compare  page  14  of  this  paper. 


■l6  UNIVERSITY  OF   MISSOURI  STUDIES  [184 


0 


ticular  as  a  type,  as  having  universal  significance.  It  is  fre- 
quently hasty  and  its  results  are  frequently  discovered  to  be  false, 
but  that  does  not  aflfect  its  nature.  The  point  to  be  emphasized 
here  is  that  induction  consists  in  making  the  leap  spoken  of,  re- 
gardless of  whether  we  have  any  warrant  for  doing  so  or  not. 
We  say,  what  is  true  of  these  particular  instances  is  true  of  their 
class,  and,  after  having  made  many  such  inferences,  we  finally 
reach  the  belief  that  nature  at  large  is  uniform.  The  belief  in 
the  general  uniformity  of  nature  is  a  late  product  in  the  history 
of  civilization,  and  is  not  even  universally  accepted  to-day.  It  is 
preceded  by,  and  grows  out  of,  the  belief  that  a  particular  in- 
stance will  repeat  itself. 

§  3.  This  brings  us  to  our  second  fundamental  ques- 
tion :  What  is  the  validity  of  the  process  of  induction  ?  What  is 
its  warrant?  Here  we  may  discuss  two  problems,  (a)  How 
can  we  reach  the  greatest  possible  certainty  in  particular  in- 
ductions?    (b)     How  can  we  prove  induction  in  general? 

(a)  Certainty  is  a  feeling.  We  feel  certain  that  a  proposi- 
tion is  true;  the  proposition  is  certain  because  it  arouses  in  us 
the  feeling  of  certainty.  What  must  we  do  to  reach  such  cer- 
tainty in  a  particular  induction?  We  increase  our  feeling  of 
certainty  in  many  ways.  We  notice  that  qualities  go  together. 
The  more  often  we  observe  it,  the  more  certain  we  feel  that  they 
will  continue  to  go  together.  When  we  observe  that  one  fails 
to  appear  the  other  fails  to  appear  also,  and  that  when  one  varies 
the  other  varies,  we  feel  still  more  certain  that  they  go  together, 
that  our  induction  is  true.  The  purpose  of  the  so-called  induc- 
tive methods  is  to  bring  this  certainty  to  the  highest  possible  de- 
gree. We  feel  most  certain  of  propositions  which  have  been 
verified  countless  times,  and  of  which  we  have  experienced  no 
contradictory  instances.     It  is  for  this  reason  that  we  strive  to 


185]  THE  PROCESS  OF  INDUCTIVE  INFERENCE         37 

subsume  all  other  propositions  under  such  propositions,  that  we 
try  to  consider  them  as  instances  of  these.  We  have  had  a  great 
deal  of  experience  with  motion,  for  example;  hence,  if  we  can 
reduce  a  phenomenon  to  motion,  we  feel  that  we  know  something 
about  it.  In  other  words,  we  reach  the  greatest  possible  cer- 
tainty for  our  particular  inductions  when  we  subsume  them  un- 
der generally  accepted  principles,  or  prove  them  deductively. 
That  is  why  sciences  become  more  and  more  deductive  in  the 
course  of  time. 

It  is  also  to  be  noted  here  that,  wherever  the  connection  is 
believed  to  be  a  causal  connection,  one  case  is  as  good  as  a  thou- 
sand. When  I  believe  that  two  phenomena  are  causally  related, 
I  am  sure  that  one  will  always  follow  the  other,  because  causal 
connection  means  a  necessary  connection,  because  the  notion  of 
cause  implies  that  when  one  phenomenon  appears  the  other  must 
somehow  appear  also.  When  I  conceive  of  a  particular  case  as 
a  case  of  causality,  when  I  say  in  this  particular  case  a  was  the 
cause  of  h,  I  do  not  need  any  other  cases  to  convince  me  that 
there  is  a  universal  relation.  I  conclude  from  one  to  many,  be- 
cause I  have  already  assumed  uniformity  by  assuming  causality. 
Similarly,  whenever  I  conceive  of  phenomena  as  necessarily  re- 
lated in  any  other  way,  one  case  is  as  good  as  a  thousand. 
When  I  see  that  the  sum  of  the  angles  of  a  triangle  is  equal  to 
two  right  angles,  having  proved  it  for  a  particular  triangle  by 
showing  that  it  follows  necessarily  from  the  definition  of  a  tri- 
angle, then  I  am  satisfied  that  it  will  be  true  of  all  triangles ;  and 
there  is  no  need  of  my  examining  any  more. 

These  cases,  however,  are  not  cases  of  induction.  When  I 
say,  this  phenomenon  caused  that  one  in  this  particular  case, 
therefore  whenever  I  have  this  phenomenon  in  other  cases  I  will 
have  the  other  also,  I  am  reasoning  deductively.  By  saying  that 
a  particular  relation  is  a  causal  relation,  I  am  implying  that  it  has 


38  UNIVEUSITY  OF  MISSOURI  STUDIES  [186 

universal  validity.  I  reason:  If  a  and  b  are  causally  related, 
then  when  a  appears  b  will  appear  also.  Now  a  and  b  are  caus- 
ally related.  Hence,  when  a  appears,  b  will  appear  also.  This 
is  deduction. 

(b)  How  can  we  prove  induction?  By  proof  we  mean 
deduction.  Our  question  therefore  means:  What  must  we 
do  in  order  to  deduce  a  conclusion  which  has  already  been  de- 
rived inductively?  In  deduction  we  consciously  draw  a  propo- 
sition from  premises  in  which  it  is  already  implied ;  we  explicate 
it.  Here  our  conclusion  will  give  us  a  feeling  of  absolute  cer- 
tainty, that  is,  we  will  feel  that  if  the  premises  are  true,  the  con- 
clusion must  be  true,  unless  we  have  made  a  mistake  in  our  rea- 
soning. It  is  not  difficult  to  construct  a  syllogism  in  which  the  in- 
ductive proposition  forms  the  conclusion.  For  example,  if  it  is 
true  that  nature  is  uniform,  that  nature  repeats  itself,  that  it  is  a 
reign  of  law,  then  we  have  a  proof  for  induction.  One  should 
remember,  however,  that  this  does  not  make  induction  deduction. 
Induction  is  induction;  by  proving  a  proposition  that  has  been 
derived  inductively,  we  do  not  make  induction  deduction,  we 
simply  apply  another  process,  deduction,  to  a  proposition  that 
has  already  been  derived  inductively.  The  process  of  proving 
the  inductive  proposition  is  not  induction,  but  deduction.  Here 
the  certainty  of  the  proof  will,  as  always,  depend  upon  the  cer- 
tainty of  the  principle  of  uniformity.  The  more  we  believe  in 
this  principle,  the  more  certain  we  shall  be  of  our  inductions, 
the  more  satisfied  we  shall  be  with  them. 

Induction,  therefore,  may  be  proved  by  assuming  the  law  of 
uniformity.  We  are  warranted  in  leaping  from  part  to  whole 
by  the  regularity,  or  orderliness,  or  uniformity  of  nature.  If  it  is 
true  that  nature  is  uniform,  that  nature  repeats  itself,  we  have 
the  right  to  conclude  from  a  few  instances  to  all  Hke  them.  The 
only  problem  here  is  to  discover  the  particular  combinations,  the 
co-existences  and  sequences  in  nature. 


187]  THE  PROCESS  OF  INDUCTIVE  INFERENCE 


39 


But  the  question  at  once  arises:  What  warrant  have  we 
for  saying  that  nature  is  uniform?  It  may  perhaps  be  said  that 
this  principle  is  a  postulate  of  thought,  and  that  it  carries  its  war- 
rant in  itself.  We  cannot  prove  its  truth,  but  we  feel  certain 
that  it  is  true ;  we  accept  it  without  cavil.  But  is  it  really  a  pos- 
tulate of  thought?  Does  everybody  really  accept  it?  Does  it 
inhere  so  in  the  nature  of  our  thought  that  we  must  accept  it  ? 

That  depends  entirely  upon  what  we  mean  by  it.  If  we 
mean  by  it  the  clearly  conscious  thought  that  nature  at  large, 
internal  and  external  nature,  is  governed  by  law,  that  it  is  a  uni- 
fied system,  then  we  cannot  regard  the  principle  as  a  postulate 
of  thought.  In  this  sense,  it  is  plainly  a  product  of  development, 
the  result  of  much  reflection  upon  the  world,  and  even  then  not 
at  all  universally  accepted.  There  are  many  persons  who  will 
not  admit  that  external  nature  is  a  closed  system,  exempt  from 
interference,  and  there  are  still  more  who  will  not  admit  that  the 
mental  realm  is  subject  to  law.  Interpreted  in  the  above  sense, 
the  principle  of  uniformity  must  be  regarded  as  the  result  of  re- 
flection upon  our  experiences.  We  have  noticed  many  particu- 
lar uniformities;  we  conclude  that  nature  at  large  is  uniform, 
that  is,  we  consciously  ground  our  proposition  upon  our  past  ex- 
periences. In  this  sense,  the  principle  of  uniformity  is  an  induc- 
tion :  Because  there  are  uniformities,  there  is  uniformity.  And 
if  we  try  to  base  the  inductive  process  upon  the  principle  thus 
understood,  we  are  really  reasoning  in  a  circle,  as  has  been  so 
often  pointed  out.  We  prove  the  uniformities  by  the  uniformity, 
and  the  uniformity  by  the  uniformities.  We  say  we  are  war- 
ranted in  inferring  from  the  particular  to  the  universal,  because 
nature  repeats  itself,  because  nature  is  uniform ;  and  we  say  we 
know  nature  is  uniform,  because  we  discover  particular  uniform- 
ities and  conclude  from  these  that  there  is  general  uniformity. 

We  may,  however,  mean  by  the  principle  of  uniformity  of 


40  UNIVERSITY  OF  MISSOURI   STUDIES  [l88 

nature  as  a  postulate  of  thought,  not  a  clear  conviction  that  na- 
ture as  a  whole  is  a  unified  system,  subject  to  law,  but  the  feel- 
ing in  every  particular  case  that  this  particular  experience,  will 
come  again.  Here  we  form  no  conception  of  nature  as  a  whole ; 
but  every  time  we  have  a  particular  experience,  we  expect  it  to 
recur.  After  having  a  particular  experience  a  number  of  times, 
we  feel  that  it  will  come  again,  we  expect  particular  things  to 
repeat  themselves.  Our  feeling  of  expectation  here  may  be 
called  a  postulate  of  thought,  and  it  becomes  the  psychological 
ground  of  our  inductive  inference.  That  is,  there  is  no  reason 
for  inferring  that  a  particular  co-existence  or  sequence  of  quali- 
ties will  recur  except  the  expectation  that  it  will  recur.  We  feel 
that  what  happens  in  this  particular  case  will  happen  so  again, 
we  expect  it  to  happen  so  again ;  we  therefore  infer  or  conclude 
that,  because  it  happened  once,  it  will  happen  again.  That  is, 
I  have  no  other  warrant  for  inferring  that  a  combination  of  qual- 
ities will  recur  than  the  feeling  of  expectation  that  it  will  do  so. 


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